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Home and Motor insurance joined at a household level using multivariate credibility

Published online by Cambridge University Press:  06 July 2020

Florian Pechon Open the ORCID record for Florian Pechon [Opens in a new window] ,
Michel Denuit  and
Julien Trufin
Florian Pechon*
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Science Université catholique de Louvain (UCLouvain), Louvain-la-Neuve, Belgium
Michel Denuit
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Science Université catholique de Louvain (UCLouvain), Louvain-la-Neuve, Belgium
Julien Trufin
Affiliation:
Department of Mathematics, Université Libre de Bruxelles (ULB), Bruxelles, Belgium
*
*Corresponding author. E-mail: florian.pechon@uclouvain.be
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Abstract

Actuarial ratemaking is usually performed at product and guarantee level, meaning that each product and guarantee is considered in isolation. Moreover, independence between policyholders is generally assumed. In this paper, we propose a multivariate Poisson mixture, with random effects correlated using a hierarchical structure, to accommodate for the dependence that may exist between unobserved risk factors across Home and Motor insurance and between policyholders from the same household. The hierarchical structure accounts for the fact that Home insurance covers the whole household, whereas Motor insurance policies are subscribed by specific policyholders within the household. The model allows to periodically correct the a priori expected claim frequencies using the reported number of claims in any of the considered products. Applications show that the impact of the number of claims reported in Motor insurance on the number of claims expected in Home insurance is larger than the other way around. Moreover, an out-of-sample analysis validates an improved predictive power. Also, the model allows to identify more rapidly the riskiest households.

Keywords

Multivariate credibilityPoisson–LogNormalA posteriori claim frequency
Type
Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 1 , March 2021 , pp. 82 - 114
Copyright
© Institute and Faculty of Actuaries 2020

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